I don't think it's a good idea or any manner of respectful to post about the contents of private messages to the public forum, even though I've given my opinion before on outrageous messages people have gotten and talked about. (They have to be pretty abusive to warrant a plea to the rest of the site imo).
That said, I personally also frown upon this site being used for the goal of some type of romantic relationship..and tbh this seems to be the mindset of a disproportionate amount of people here..it's like "either I ctb or get me a gf/bf". Or they combine both notions on the partners thread, which I stay away from for good reason. That is the risk in getting too close with some people here, I'm personally not worried about it, but other people should be. There are predators, scammers, and just plain lonely, desperate people looking for something other than friendship. A lot of the time, at a very fast pace..if you are oblivious then it can take you by surprise. And if you're not interested, it won't be pleasant.
But in that case, I would just be straight with the person messaging you and then move on. Ignore them if need be. They could have malicious intent or they could just be the typical isolated, socially starved person who gets overly attached to anyone who shows them attention. It's a common phenomenon.
No need to be cruel but no need to be shy about shutting it down either. It's not really something that requires making a thread about, even if they get out of hand, just report them. Everyone here already has a reason to ctb, let none of us flatter ourselves in thinking we would suddenly be the sole reason for someone here offing themselves. I don't think a private, respectful rejection would push them over the edge but telling everyone else about it, even without naming names...well that can put a person into a panic. I think it's a bad idea to be completely frank with you.
You can easily clear things up with this person in private, and like I said, bring it to a mod's attention if the person shows relentless fervor in pursuing or blaming you.
Edit: Keep in mind I only read the first page of responses. I didn't realize there were 3 more until after commenting.